IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v40y2020i3d10.1007_s10878-020-00611-2.html
   My bibliography  Save this article

Maximum weight induced matching in some subclasses of bipartite graphs

Author

Listed:
  • B. S. Panda

    (Indian Institute of Technology Delhi)

  • Arti Pandey

    (Indian Institute of Technology Ropar)

  • Juhi Chaudhary

    (Indian Institute of Technology Delhi)

  • Piyush Dane

    (Indian Institute of Technology Delhi)

  • Manav Kashyap

    (Indian Institute of Technology Delhi)

Abstract

A subset $$M\subseteq E$$ M ⊆ E of edges of a graph $$G=(V,E)$$ G = ( V , E ) is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an induced matching if G[M], the subgraph of G induced by M, is the same as G[S], the subgraph of G induced by $$S=\{v \in V |$$ S = { v ∈ V | v is incident on an edge of $$M\}$$ M } . The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. Given a graph G and a positive integer k, the Induced Matching Decision problem is to decide whether G has an induced matching of cardinality at least k. The Maximum Weight Induced Matching problem in a weighted graph $$G=(V,E)$$ G = ( V , E ) in which the weight of each edge is a positive real number, is to find an induced matching such that the sum of the weights of its edges is maximum. It is known that the Induced Matching Decision problem and hence the Maximum Weight Induced Matching problem is known to be NP-complete for general graphs and bipartite graphs. In this paper, we strengthened this result by showing that the Induced Matching Decision problem is NP-complete for star-convex bipartite graphs, comb-convex bipartite graphs, and perfect elimination bipartite graphs, the subclasses of the class of bipartite graphs. On the positive side, we propose polynomial time algorithms for the Maximum Weight Induced Matching problem for circular-convex bipartite graphs and triad-convex bipartite graphs by making polynomial time reductions from the Maximum Weight Induced Matching problem in these graph classes to the Maximum Weight Induced Matching problem in convex bipartite graphs.

Suggested Citation

  • B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 2020. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 713-732, October.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:3:d:10.1007_s10878-020-00611-2
    DOI: 10.1007/s10878-020-00611-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00611-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-020-00611-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 0. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.
    2. Hao Chen & Zihan Lei & Tian Liu & Ziyang Tang & Chaoyi Wang & Ke Xu, 2016. "Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 95-110, July.
    3. Tian Liu & Zhao Lu & Ke Xu, 2015. "Tractable connected domination for restricted bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 247-256, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 0. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.
    2. D. H. Aneesh & A. Mohanapriya & P. Renjith & N. Sadagopan, 2022. "Steiner tree in k-star caterpillar convex bipartite graphs: a dichotomy," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1221-1247, September.
    3. Hao Chen & Zihan Lei & Tian Liu & Ziyang Tang & Chaoyi Wang & Ke Xu, 2016. "Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 95-110, July.
    4. Henning, Michael A. & Ananchuen, Nawarat & Kaemawichanurat, Pawaton, 2020. "Traceability of connected domination critical graphs," Applied Mathematics and Computation, Elsevier, vol. 386(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:40:y:2020:i:3:d:10.1007_s10878-020-00611-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.